Szeged and Mostar root-indices of graphs

Brezovnik, Simon (author), Dehmer, Matthias (author), Tratnik, Niko (author), Žigert Pleteršek, Petra (author)

Various distance-based root-indices of graphs are introduced and studied in the present article. They are obtained as unique positive roots of modified graph polynomials. In particular, we consider the Szeged polynomial, the weighted-product Szeged polynomial, the weighted-plus Szeged polynomial, and the Mostar polynomial. We derive closed formulas of these polynomials for some basic families of graphs. Consequently, we provide closed formulas for some root-indices and examine the convergence of sequences of certain root-indices. Moreover, some general properties of studied root-indices are stated. Finally, numerical results related to discrimination power, correlations, structure sensitivity, and abruptness of root-indices are calculated, interpreted, and compared to already known similar descriptors.

• Language: English
• Keywords: Szeged index, Szeged polynomial, Mostar polynomial, root-index, discrimination power, sensitivity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2023
• Number of pages: 11 str.
• Numbering: Vol. 442, art. 127736
• PID: 20.500.12556/RUL-168616
• UDC: 519.17
• ISSN on article: 0096-3003
• DOI: 10.1016/j.amc.2022.127736
• COBISS.SI-ID: 139442179
• Publication date in RUL: 18.04.2025

Record is a part of a journal

• Title: Applied mathematics and computation
• Shortened title: Appl. math. comput.
• Publisher: Elsevier
• ISSN: 0096-3003
• COBISS.SI-ID: 24983808

Licences

• License: CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
• Link: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Description: The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.

Projects

• Funder: ARRS - Slovenian Research Agency
• Project number: P1-0297
• Name: Teorija grafov

• Funder: ARRS - Slovenian Research Agency
• Project number: BI-AT/20-21-001
• Name: Topological descriptors and entropies in networks